Rinse the chicken pieces well with cold water and pat dry with paper towels. Sprinkle both sides of chicken with salt and smoked paprika. Dredge seasoned chicken in flour. Shake off excess and set chicken aside.

Melt butter in large, deep skillet over medium heat. When butter starts bubbling, add minced shallots. Cook for 4-5 minutes until softened. Add chicken pieces to pan with shallots and let the flour on the chicken cook to a nice, dark (but not burnt) crust on all sides (start with the largest pieces so they have a little more time to cook). (You are basically building a roux here.)

Mix vinegars, stock, tomato paste, apple cider or maple syrup and pour mixture over chicken. Scrape browned bits from bottom of pan up into braising liquid. Stir in thyme. Bring the heat down to low, cover pan, and let chicken simmer for an hour. Stir from time to time. After an hour, season with salt and pepper to taste and serve over mashed potatoes.